The VIMOS Public Extragalactic Redshift Survey (VIPERS): Gravity test from the combination of redshift-space distortions and galaxy-galaxy lensing at 0.5 < z < 1.2

We carry out a joint analysis of redshift-space distortions and galaxy-galaxy lensing, with the aim of measuring the growth rate of structure; this is a key quantity for understanding the nature of gravity on cosmological scales and late-time cosmic acceleration. We make use of the final VIPERS redshift survey dataset, which maps a portion of the Universe at a redshift of z similar or equal to 0.8, and the lensing data from the CFHTLenS survey over the same area of the sky. We build a consistent theoretical model that combines non-linear galaxy biasing and redshift-space distortion models, and confront it with observations. The two probes are combined in a Bayesian maximum likelihood analysis to determine the growth rate of structure at two redshifts z = 0.6 and z = 0.86. We obtain measurements of f sigma(8)(0.6) = 0.48 +/- 0.12 and f sigma(8)(0.86) = 0.48 +/- 0.10. The additional galaxy-galaxy lensing constraint alleviates galaxy bias and sigma(8) degeneracies, providing direct measurements of f and sigma(8): [f (0.6), sigma(8)(0.6)] = [0.93 +/- 0.22, 0.52 +/- 0.06] and [f (0.86), sigma(8)(0.86)] = [0.99 +/- 0.19, 0.48 +/- 0.04]. These measurements are statistically consistent with a Universe where the gravitational interactions can be described by General Relativity, although they are not yet accurate enough to rule out some commonly considered alternatives. Finally, as a complementary test we measure the gravitational slip parameter, E-G, for the first time at z > 0.6. We find values of (E) over bar (G)(0.6) = 0.16 +/- 0.09 and (E) over bar (G)(0.86) = 0.09 +/- 0.07, when E-G is averaged over scales above 3 h(-1) Mpc. We find that our EG measurements exhibit slightly lower values than expected for standard relativistic gravity in a Lambda CDM background, although the results are consistent within 1-2 sigma.